DISTRIBUTIONAL LINKAGES BETWEEN EUROPEAN SOVEREIGN BOND AND BANK ASSET RETURNS Julio Galvez and Javier Mencía CEMFI Working Paper No. 1407 November 2014 CEMFI Casado del Alisal 5; 28014 Madrid Tel. (34) 914 290 551 Fax (34) 914 291 056 Internet: www.cemfi.es We would like to thank Dante Amengual, Manuel Arellano, Stéphane Bonhomme, Julio A. Crego, Juan Carlos Escanciano, Iván Fernández-Val, Christian Hellwig, Gur Huberman, Jesús Saurina, Enrique Sentana, Frank Smets and seminar audiences at CEMFI for helpful comments and suggestions. All remaining errors and omissions are our own responsibility. The views expressed in this paper are those of the authors, and do not reflect those of the Bank of Spain.
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We would like to thank Dante Amengual, Manuel Arellano, Stéphane Bonhomme, Julio A. Crego, Juan Carlos Escanciano, Iván Fernández-Val, Christian Hellwig, Gur Huberman, Jesús Saurina, Enrique Sentana, Frank Smets and seminar audiences at CEMFI for helpful comments and suggestions. All remaining errors and omissions are our own responsibility. The views expressed in this paper are those of the authors, and do not reflect those of the Bank of Spain.
CEMFI Working Paper 1407 November 2014
DISTRIBUTIONAL LINKAGES BETWEEN EUROPEAN SOVEREIGN BOND AND BANK ASSET RETURNS
Abstract We analyse the dependence between sovereign bonds’ and banks’ asset return distributions with a large panel of European data from 2001 to 2013. Using quantile regressions, we identify nonlinear contemporaneous and lagged dependence. As a result, shocks to crisis-hit sovereign bonds have contemporaneous effects on the whole distribution of banks’ returns, as well as a persistent impact in the tails. Our results offer relevant insights about the relationship between banking and sovereign crises. In particular, during the recent financial crisis, banks’ asset return distributions have lower means and fatter tails than in the absence of a simultaneous sovereign crisis. JEL Codes: G15, G21, F34. Keywords: Quantile regressions, nonlinear dependence, counterfactual analyses, systemic risk. Julio Galvez CEMFI [email protected]
The European financial and sovereign debt crises have generated interest in the re-
lationship between sovereign credit risk and financial sector risk, as investor concerns
on sovereign creditworthiness and bank solvency continue to plague European Union
(EU) member countries on the periphery (Greece, Ireland, Italy, Portugal, and Spain
- hereafter known as GIIPS). The crisis, which manifested in early April 2007, became
full-blown with the collapse of Lehman Brothers in mid-September 2008. The credit
crunch then hit Europe’s banking sector nearly two weeks after, and precipitated a wave
of bank rescue and stimulus packages that were initiated by major EU governments to
shore up their economies. Meanwhile, another crisis arose as several European Monetary
Union (EMU) member countries, and in particular, the GIIPS, ran budget deficits due to
increased government spending and weak tax revenues. The rising amount of sovereign
debt led to a widening differential between the GIIPS countries and the more stable EMU
countries like Germany, as illustrated in Figure 1. Investors became concerned about the
ability of these countries to cover maturing debt and interest payments, which resulted
in credit rating downgrades; the euro depreciated, and share prices further declined as a
response.
In light of the financial crisis, numerous empirical studies have placed considerable
attention to the interdependence between sovereign bonds and banks’ asset returns.
Alter and Schuler (2012) find that prior to the banking crisis, contagion disperses from
banks to the sovereign credit default swap (CDS) market, while after the banking crisis, a
financial sector shock affects the sovereign more strongly in the short run than in the long
run. Ejsing and Lemke (2011) study the relationship between bank and sovereign CDS
premia and find that the variation between the two can be explained by a single common
risk factor. Dieckmann and Plank (2012), meanwhile, find negative correlation between
financial sector and sovereign CDS spreads while rescue packages are being instituted,
and a positive correlation afterwards. Acharya and Steffen (2014) argue that bank risks
reflect a “carry trade” behavior in that banks appeared to have taken long positions in
GIIPS sovereign bonds, which were funded by short-term lending in wholesale markets.
Finally, Gennaioli et al. (2013) find that the correlation between sovereign bonds and
future bank loans are positive in normal times, while negative in crisis times.
1
The studies mentioned earlier have relied on standard regression techniques to analyse
this effect, which implies that they have only considered the conditional mean of bank and
bond return distributions. The main objective of this paper, in contrast, is to investigate
this interdependence on the whole distribution of bank asset returns and sovereign bond
returns. There are two reasons for focusing on distributions of bank and bond returns as
opposed to focusing just on the conditional mean. First, considerable research has shown
that investor preferences go beyond mean and variance in their portfolio optimisation
decisions to higher-order moments. In particular, investors care about potential portfolio
losses, more known as downside risk, which is a function of higher-order moments such
as skewness and kurtosis.1 Second, the recent financial crisis has emphasised the need to
quantify systemic risk. While numerous quantitative measures have been developed in
response, the more prominent ones focus on the tails of the asset returns’ distributions,
a feature that cannot be captured by standard regressions.2 Though we do not propose
a systemic risk measure, our empirical analysis aims to capture the transmission of risk
from sovereign bonds across the conditional distribution of bank returns, and similarly,
from bank returns across the conditional distribution of sovereign bond returns.
In this regard, we employ a multivariate quantile regression model to directly study
the contemporaneous linkages between European sovereign bond and bank return distri-
butions. We consider an extensive database with weekly data from 2001 to 2013, covering
27 major European banks and the sovereign returns from their countries. Quantile re-
gression offers the following advantages over the standard regression framework. First,
as it is a semi-parametric technique, it does not require a distributional assumption on
bank asset returns and sovereign bond returns; this implies that the regression results
are robust to non-normality and to outliers. Second, quantile methods are efficient in the
use of data. Third, the flexibility of quantile regression methods permits a more com-
prehensive analysis of the impact of bond returns on the entire conditional distribution
of bank asset returns, and vice-versa.
1Harvey and Siddique (2000) argue that investors like positive skews (big returns) and dislike negativeskews (big losses), and that these must be taken into account when making investment decisions. Harveyet al. (2010) provide an analysis of portfolio choice taking into account higher-order moments in theutility function of investors. Kelly and Jiang (2014), meanwhile, analyse the impact of tail risk on assetprices.
2Prominent tail risk measures include CoVaR by Adrian and Brunnermeier (2011), Marginal Ex-pected Shortfall by Acharya et al. (2012) and its dynamic counterpart proposed by Brownlees andEngle (2010).
2
The results of the quantile regression estimates indicate that there exists nonlinear
dependence between sovereign bond and bank asset returns, a feature not captured by
standard regression techniques. Specifically, the results suggest a contagion effect from
the peripheral sovereign bond returns across the return distribution of banks headquar-
tered in non-GIIPS countries. Moreover, the results capture a strong transmission of
risk from sovereign bond to bank asset returns of GIIPS countries. We then recover the
the conditional distributions of bank returns, and analyse how they shift in response to
shocks from bond returns. We find that a negative shock on the GIIPS sovereign bonds
yields for non-GIIPS banks a lower expected return, and a distribution that is more
negatively skewed and has fatter left tails. We take this as evidence of contagion from
the GIIPS sovereign bonds to non-GIIPS banks’ asset returns.
We extend the analysis to study the evolution of the conditional distributions over
time through a quantile vector autoregressive framework. The quantile regression results
confirm the importance of contemporaneous dependence between sovereign bond and
bank asset returns; we also find that the past history of bond returns influences the
shape of the distribution of bank asset returns. We then analyse the impact of multi-
period negative sovereign shocks on the conditional quantile functions, and in turn, the
conditional distribution of bank asset returns over time. We find that a negative shock
to the peripheral sovereign bonds yields an increase in the volatility of bank asset returns
over the long run. In contrast, a negative shock on the German bond returns only shifts
banks’ return distributions in the short run. We finally analyse the sensitivity to the crisis
of our results. We find that the transmission of risk between peripheral sovereign bond
returns to bank asset returns of non-GIIPS countries was stronger during crisis periods
compared to non-crisis periods. We then compute for the unconditional marginal density
of a bank’s asset returns in the scenario that the sovereign crisis had not occurred. In
general, the sovereign crisis increased banks’ riskiness, as shown by return distributions
that had lower expected returns, higher volatility and fatter tails.
The rest of the paper is as follows. In Section 2, we discuss the data used and provide
summary statistics. We analyse the contemporaneous linkages between sovereign bond
and bank asset returns in Section 3. We also discuss the kernel interpolation methodology
and the sensitivity analysis performed. We consider an autoregressive framework in
Section 4 and analyse the evolution of return distributions over time. In Section 5, we
3
analyse the sensitivity of the results we have obtained to crisis and non-crisis periods.
Finally, Section 6 concludes. Some technical discussion of the methods used for the
empirical analysis pursued in this paper are gathered in appendices.
2 Data and summary statistics
2.1 Dataset construction
We construct a dataset with information obtained from Datastream and Bloomberg
to compute bank asset returns and sovereign bond returns. The information covers the
period from January 3, 2001 to November 6, 2013. The data comprises 27 major cross-
border banks in Europe, a list of which is provided in Appendix A. Out of the banks in
the sample, ten are headquartered in peripheral countries, while 17 are headquartered
outside of the GIIPS countries. There are 14 countries represented in the dataset; ten
are in the Eurozone,3 while the remaining countries are Denmark, Sweden, Switzerland,
and the United Kingdom.4
We compute weekly bank asset returns from publicly available market information
such as bank equity prices, market-to-book equity ratio, and the book value of total
assets from Datastream.5 We follow Adrian and Brunnermeier (2011) in specifying bank
asset returns as the return of market-valued total financial assets denominated in euros
through the following definition. Denote by MEt,Bithe market value of bank i’s total
equity, and by LEVt,Bithe ratio of total assets to book equity. We define the daily return
of market-valued total assets, yt,Biby
yt,Bi=At,Bi
− At−1,Bi
At−1,Bi
where At,Bi= MEt,Bi
· LEVt,Bi. Note that LEVt,Bi
= BAt,Bi/BEt,Bi
, where BAt,Biis
the book-valued total assets of the institution and BEt,Biis the book value of a bank’s
equity; hence, At,Bi=MEt,Bi
·LEVt,Bi= BAt,Bi
· (MEt,Bi/BEt,Bi
). Thus, we can apply
3The Euro area countries included in the sample are: the GIIPS countries, Austria, Belgium, France,Germany, and the Netherlands.
4We calculate the euro-denominated returns of non-Euro area banks and sovereign bonds by convert-ing the relevant variables into euros using spot exchange rate data obtained from the Pacific ExchangeRate database.
5Save for the book value of total assets, which we observe at a quarterly frequency, we observe therest at a daily frequency and take the observations on Wednesday to create the variable. We computeweekly bank asset returns as some equity prices were illiquid during certain periods.
4
the market-to-book equity ratio to transform book-valued total assets into market-valued
total assets.
Meanwhile, we construct euro-denominated sovereign bond returns for the countries
in the dataset by a first-order approximation using ten-year weekly sovereign bond yields
obtained from Datastream and bond duration data obtained from Bloomberg. More
formally, we denote by Durt,Sjthe duration, and by Zt,Sj
, the yield on the ten-year
sovereign bond of country j. We first compute for the modified duration of the bond,
ModDt,Sjas
ModDt,Sj=
Durt,Sj(
1 + Zt,Sj/100
)
We finally calculate weekly sovereign bond returns, yt,Sjfrom the following formula:
yt,Sj= −ModDt−1,Sj
·(
Zt,Sj− Zt−1,Sj
)
2.2 Summary statistics
Tables 1 and 2 show some summary statistics about sovereign bond returns. From
Table 1, we observe that GIIPS countries generally have bond return distributions with
negative means, negative skewness, and fat tails. Non-GIIPS countries, on the other
hand, generally have bond return distributions with positive means, negative skewness
and tails that are less fat than those of GIIPS sovereign bond returns.6 Table 2 shows
the correlations between the GIIPS and the German sovereign bonds, divided into three
phases: the pre-banking crisis phase, which is the period prior to August 2007, the onset
of the banking crisis in Europe; the banking crisis phase, which is from August 2007
to November 2009, when the newly-elected Greek government disclosed a deficit that
doubled the previous official figure; and the sovereign crisis phase, which, for parsimony,
we compute until the first bailout of Greece by the troika.7 The table shows that before
the financial crisis occurred, German and peripheral sovereign bonds were highly corre-
lated, which might suggest that investors perceived those bonds as similar despite major
economic differences. As the banking crisis unfolded, however, German sovereign bonds
and peripheral sovereign bonds became less correlated. Finally, when the sovereign debt
6Performing the Jarque-Bera test for normality confirms the intuition that bond return distributionsare non-Gaussian.
7The troika is composed of the European Community (EC), the International Monetary Fund (IMF),and the European Central Bank (ECB).
5
crisis occurred, we see that the correlations between German sovereign bonds and the
periphery turned negative, showing the divergence of the countries within the Euro area.
Finally, Figure 2 shows the predicted GARCH(1,1) asset return volatilities of BNP
Paribas, Deutsche Bank and Banco Santander, and the corresponding sovereign bond
yields of the countries these banks are headquartered in. The figure highlights the
relationship between banks’ asset returns and movements in the sovereign debt market.
In particular, we find that the volatility of banks’ asset returns reflects two crises: the
global financial crisis (from 2008 to 2009), and the sovereign debt crisis (from 2011
to 2012), each with a different impact for different banks. On the one hand, French
and German sovereign bond yields exhibit a decreasing trend; on the other hand, the
sovereign yields from peripheral sovereign countries, here represented by Spain, started
increasing in the financial crisis, but they did not reach huge levels until the sovereign
crisis exploded. We observe that, save for Deutsche Bank, bank asset return volatilities
have a similar evolution. In contrast, some countries suffer higher yields while others
enjoy increasingly cheaper access to credit.
3 Contemporaneous dependence between bank and
bond returns
As the goal of the paper is to study the linkages across sovereign bond and bank
return distributions, it is relevant to consider the joint distribution of bank and bond
returns, fB,S(yt,B,yt,S|It−1), where yt,B and yt,S denote the vectors of banks and bonds
returns, respectively, and It−1 denotes the information known at time t − 1. We can
where qt,B(θ) (qt,S(θ)) is the vector of θ-th quantiles of banks (sovereign bond) re-
turns. This specification takes into account the interplay between bank and bond re-
turns through the parameterisation of matrices Abs(θ), Asb(θ) and Ass(θ). The vectors
of coefficients cB(θ) and cS(θ), the matrices Abs(θ), Asb(θ) and Ass(θ), and the scalar
parameters ν(θ) and φ(θ) are all constant for a given quantile level θ. However, we
consider different constant parameters for each quantile level. Notice that the linear de-
pendence implied by the Gaussian distribution would yield constant parameters across
quantiles, except for the intercept. In this sense, we can argue that there is nonlinear
dependence if our estimates differ from those of a standard regression. We can interpret
quantile models (3) and (4) as the Exposure CoVaR of banks conditional on the situ-
ation of the sovereign for (3), and the Exposure CoVaR of sovereign bonds conditional
on the situation of the banking system for (4), respectively.8 As opposed to Exposure
CoVaR, which focuses on the tail of the distribution of bank asset returns conditional
on sovereign bond returns, we consider the entire distribution of bank asset returns con-
ditional on sovereign bond returns (and vice-versa). By characterising the conditional
distributions, we can analyse how shocks on key variables have an impact on the shape
of the distribution, which we discuss in section 3.2.
8As in Adrian and Brunnermeier (2011), we define CoV aRi|jC(Xj)q as the Value-at-Risk (VaR) of
institution i conditioning on some event C(Xj) of an institution j. That is, CoV aRi|C(Xj)θ is implicitly
defined by the q-quantile of the conditional probability distribution Pr[Xi ≤ CoV aRi|C(Xj)θ |C(Xj)] = θ.
7
For parsimony, we parameterise the matrices Abs(θ), Asb(θ) and Ass(θ) as sparse
matrices; that is, we focus on the most relevant effects, and set the remaining elements
of the matrices to zero. In addition, we employ a panel structure by which each effect has
a common coefficient across the cross-sections of banks and bonds. The dimensions of
Abs(θ), Asb(θ) and Ass(θ) are n×m, m×n, andm×m, respectively, as there are n banks
and m bonds in the sample. We consider different coefficients depending on whether the
countries are GIIPS or not. In addition, we allow German sovereign bonds and banks
to have an additional impact on all other banks and countries. The developments in the
German market have been widely perceived as a relevant fear gauge during the crisis,
as noted by Acharya and Steffen (2014) and Angeloni and Wolff (2012). For instance,
flight-to-quality movements out of crisis-hit markets and into German assets have been
common at the points when the crisis aggravated.
We first outline the effects that enter in Abs(θ):
• GIIPS bond returns to non-GIIPS bank returns: α.
• German bond returns to non-German bank returns: β.
• Own bond effect to banks headquartered in the country: γ on the cells of non-
GIIPS banks and τ for GIIPS banks’ returns.
The effects captured in Asb(θ) can be summarised as:
• GIIPS banks to non-GIIPS bond returns: η.
• German banks to non-German bond returns: ω.
• Effect of banks headquartered in a country to their own sovereign bond: κ on the
cells of non-GIIPS bonds and π for GIIPS bonds.
Lastly, Ass(θ) only contains the contemporaneous effect of GIIPS bonds on non-
GIIPS bonds (ψ).
Figure 3 graphically summarises the effects that we consider on GIIPS countries,
Germany and non-GIIPS countries, respectively. With this specification, we substan-
tially extend those employed by previous empirical studies to study dependence on the
whole conditional distribution, and not just on its conditional mean.
8
To focus the discussion, consider a simplified version of quantile models (3) and (4)
with only three countries with one bank at each of them. The countries would be a
non-GIIPS country, Germany, and a GIIPS country, ordered in this way in the matrices.
Then, we would have
Abs(θ) =
γ β α0 γ α0 β τ
, Asb(θ) =
κ ω η0 κ η0 ω π
,Ass(θ) =
0 0 ψ0 0 ψ0 0 0
.
Once again, it is important to stress that most of the effects we attempt to capture
are homogeneous within each of the categories we classified earlier (i.e., the effect of the
German sovereign bond is the same for a French-headquartered bank and a Spanish-
headquartered bank). In principle, we could allow for the effects we are capturing to
vary across individual banks (and in turn, individual sovereigns); this, however, would
increase the computational burden of estimating the system we consider in this empirical
study. Moreover, following the empirical studies earlier mentioned, we are interested in
common effects across the European financial system, not in the particular determinants
of a given bank. These common effects are directly related to systemic risk, as they may
bring a collapse of the whole financial system.
We consider a panel of 41 dependent variables across the time period earlier specified
(as we have 27 banks headquartered in 14 countries). We use the whole sample for
all countries except for Greece, Ireland and Portugal. For these latter countries, we
only use data prior to their respective bailouts by the troika to avoid using data from
intervened economies.9 As usual in quantile regressions, we estimate the parameters by
exploiting the quasi maximum likelihood properties of the asymmetric double exponential
distribution (see White et al., 2013).10 This permits us to explicitly study the dependence
structure for each bank and sovereign, and analyse how changes in each of the effects
of interest affect the conditional distribution. We estimate the parameters of interest
by performing quantile regressions from the 10th to the 90th deciles. We then compare
the resulting estimates to those of an equivalent OLS regression. In the subsequent
discussion of results, we refer to (3) and (4) as the bank and bond quantile models,
respectively.
9The troika first bailed out these countries on the following dates: 2nd May 2010 (Greece), 28thNovember 2010 (Ireland), and 16th May 2011 (Portugal).
10Appendix B.1 explains in more detail the econometric model specification and the estimation pro-cedure.
9
Tables 3 and 4 present the results for the bank quantile model and the bond quantile
model, respectively. For brevity, we present the results of the OLS regression, and
five different quantiles that provide a depiction of the whole conditional distribution of
returns. We focus first on Table 3, which discusses the results for the bank equation (3).
Both the OLS and quantile regressions suggest that non-GIIPS banks have a positive
and significant exposure to peripheral sovereign bonds, while non-German banks have a
negative and significant exposure to German bonds. Hence, a deterioration of peripheral
sovereign debt is directly propagated across the financial system. In contrast, it is a
rise in German bond returns that deteriorates the return distributions of non-German
banks. This latter effect seems to be more related to flight-to-quality effects: banks
returns increase when German sovereign prices fall, probably as demand for a safe asset
diminishes. The own bond effect for non-GIIPS banks is also negative and significant,
which seems to imply that banks in these countries have a negative and significant
exposure to their own bond, in line with what happens to the German bond effect.
Meanwhile, the own bond effect for GIIPS banks is positive and significant; moreover,
the magnitude of this dependence is bigger (in absolute value) than the same effect for
non-GIIPS banks.
The results obtained suggest that nonlinear dependence emerges when we consider
the distributional impact of sovereign bond returns on bank asset returns. For instance,
the GIIPS bond effect on non-GIIPS banks is weaker at the extreme left tail. This result
suggests that a negative shock to GIIPS countries reduces the likelihood of positive gains
in non-GIIPS banks returns more than it increases the likelihood of extreme negative
returns. We can assess nonlinearities in greater detail in Figure 4, which shows the
graphs of the OLS and quantile regression coefficients for each of the effects of interest
in the bank equation, with the corresponding 90% confidence intervals. The differences
between the coefficients from OLS and quantile regressions confirm that sovereign bond
returns have a nonlinear impact across the distribution of bank asset returns, though
the precise form varies depending on the coefficient. For instance, the graphs indicate
that for the German bond effect and the own bond effects, the plots are somewhat
hump-shaped, while for the GIIPS bond effect, the graph is weakly increasing.
We now turn on to Table 4, which shows that the dependence of bond returns on
bank returns is weaker than that of bank returns on bond returns. Only three channels
10
turn out to be significant: the German bank effect, the own bank effect for non-GIIPS
countries, and the GIIPS bond to non-GIIPS bond effect. The former two exhibit the
same negative sign as that of the corresponding bond effect in the bank equation. Thus,
flight-to-quality effects seem to be at play in non-GIIPS countries, but not in peripheral
Euro area countries. The coefficients of GIIPS to non-GIIPS bonds, meanwhile, are
positive and significant throughout the distribution. This result suggests that there is a
contagion effect from GIIPS to non-GIIPS sovereigns. Figure 5, meanwhile, shows the
graphs of the OLS and quantile regression coefficients in the bond equation (4), with the
corresponding 90% confidence intervals. For the GIIPS bank effect and the own bank
effect for GIIPS countries, we find that the graphs are almost flat, and close to the OLS
estimates, as opposed to the corresponding effects in the bank equation. As for the other
coefficients, we find that the graphs are clearly nonlinear, and are significantly different
from OLS estimates. The precise form of nonlinearities, as in the bank equation (3),
depends on the coefficient. The German bank effect, for instance, has a graph that is
relatively constant. The graphs of the own bank effect for non-GIIPS countries, and
the GIIPS bond to non-GIIPS bond effects, meanwhile, appear to have a hump shape.
Many of the graphs, though, have steeper slopes at the extreme tails of the distribution,
which clearly suggests that the dependence is stronger at the extreme tails than at the
rest of the distribution.
3.2 Conditional densities and impulse responses
The main insight from the quantile regression results is that sovereign bond returns
have a significant, and in some cases, nonlinear impact across the whole conditional
distribution of bank asset returns. In order to understand the implications of these
effects, it is interesting to recover the cumulative distribution function of bank asset
returns conditional on sovereign bond returns from the conditional quantile functions.11
We could then analyse more easily the response of the distribution to changes in some
key variables that figured in the financial crisis.
There are several alternatives by which one could recover the conditional density
of a bank’s asset returns. For instance, one could perform quantile regressions on a
11An issue that comes up with recovering the conditional distribution is the quantile crossing prob-lem, of which a solution is provided by Chernozhukov et al. (2010); this method involves a monotonerearrangement of the conditional quantile functions. For most of the banks and bonds in the sample,quantile crossings occur up to at most 0.03 percent of the time.
11
sufficiently large number of quantiles. Another procedure would be to perform cubic
interpolation on the conditional quantile functions. In both cases, however, the resulting
conditional cumulative distribution function (c.d.f.) might not be monotone. With these
in mind, we prefer to resort to a weighted kernel interpolation methodology where we
find the kernel that best fits the grid of quantile points in our estimation.12 Specifically,
we consider the kernel c.d.f.
GBi|S(x|yt,S, It−1) =
np∑
j=1
wjΦ
(
x− qt,Bi(θj)
h
)
, (5)
where Φ(·) is the standard Gaussian c.d.f., np is the number of points and h is the
smoothing parameter.13 We calculate the weights wBi= (w1, . . . , wnp
)′ that minimise
the squared distance between the quantile level and its associated c.d.f.:
wBi= argmin
wBi
np∑
k=1
[
θk −GBi|S(qt,Bi(θk)|yt,S, It−1)
]2such that
np∑
j=1
wj = 1. (6)
Finally, by differentiation of (5), we obtain the conditional density
gBi|S(x|yt,S, It−1) =1
h
np∑
j=1
wjφ
(
x− qt,Bi(θj)
h
)
, (7)
where φ(·) is the standard normal density function. One advantage of our methodology
is that, by construction, the conditional c.d.f. is smooth and monotone, which alleviates
the worry that differentiation will result in an unstable probability density function.
We use this methodology to analyse the impact of sovereign bond returns on the
conditional density of a bank’s asset returns at two different dates: a pre-crisis date
(June 2007, two months before the beginning of the financial crisis), and a crisis date
(December 2009, after the Greek unexpected debt announcement). The analysis consists
of the following procedure. First, we obtain the actual conditional density of a given bank
on these two dates, gBi|S(x|yt,S, It−1), by setting yt,S to the actual values of the covariates
on these dates. Second, we compute a stressed conditional density, gBi|S(x|yt,S, It−1),
where yt,S = yt,S − σe′; σ is the magnitude of the shock, while e is a vector with ones
12Gallant et al. (1992) compute unconditional densities and moments implied by these densities usingkernel-based methods to analyse contemporaneous movements in stock prices and trading volume; asopposed to our study, they are not interested in specific channels by which these comovements occur.Escanciano and Goh (2014), meanwhile, use kernel-based methods to perform specification tests forlinear quantile regressions.
13We compute the bandwidth as: h = 1.06min{s, r}n−1/5p , where s is the standard deviation and r,
the interquartile range, of the quantile functions.
12
on the elements where the shock is applied, and zeros otherwise. We finally compare
the two conditional densities graphically. The interest is on studying the impact of the
following shocks: (i.) a negative shock on the GIIPS sovereign bonds; (ii.) a negative
shock on the German sovereign; and (iii.) a negative shock on the home sovereign bond.
Figure 6 illustrates the results for BNP Paribas, as the results for other non-GIIPS
banks are similar. In general, the crisis conditional densities (right panels) have clearly
shifted to lower returns with respect to the pre-crisis ones (left panels). Figures 6a and
6b show the change in the density of BNP Paribas if there is a simultaneous negative
shock to all the GIIPS sovereign bond returns equal to their historical standard devia-
tion, weighted by the relative economic size of each country.14 We find that the return
distribution shifts to the left (implying a lower expected return). The effect is slightly
asymmetric, as the density on the right tail decreases more than the left tail increases.
The results, hence, suggest a small contagion effect from peripheral sovereign debt to
non-GIIPS banks. Figure 6c and 6d, meanwhile, show the impact of a negative shock
of the German bond. We find that a negative shock on the German bond shifts the
distribution to the right and reduces the left tail of the distribution. This effect is clearly
larger than the impact of the GIIPS shock. Finally, the last two panels show the impact
of the French sovereign bond return on BNP Paribas. The results obtained show that a
negative shock on the home sovereign bond does not seem to have a significant impact
on non-GIIPS bank returns distributions. This result stands in contrast to Figure 7,
which illustrates that a shock on the own bond for Banco Santander has a larger impact
on its return distribution.
4 Modelling persistence with autoregressive quan-
tiles
It is well-established in the empirical finance literature that financial time series
exhibit time-varying volatility. Hence, one might be interested in analysing how the
conditional distributions of bank asset returns (and similarly, of sovereign bond returns)
evolve over time. In this section, we extend the model that we earlier analysed into
a quantile vector autoregressive framework, and study how shocks in the key variables
14The contribution of each GIIPS country to the GIIPS bond shock is proportional to its real grossdomestic product (GDP), which we obtained from Eurostats.
13
analysed in the previous section have an impact on the conditional distribution of bank
asset returns.
4.1 Quantile autoregressive model specification and estimation
results
We consider the following quantile autoregressive model:
The decomposition above requires two important objects for the analysis performed in
this section. The first is gBi|S(·), the conditional density of bank asset returns, which we
obtain by the kernel density interpolation described in section 3.2. The second is hS(·),the marginal density of sovereign bond returns. By assuming that hS(·) is multivariate
Normal, we obtain a closed-form solution for the marginal density of a bank, hBi(·),
which we outline in detail in Appendix C. Specifically, we obtain the actual marginal
density of bank i by integrating over the crisis marginal distribution of sovereign bonds:
yt,S ∼ N (µC ,ΣC), estimated with the crisis sub-sample. In contrast, to obtain the coun-
terfactual marginal density of bank i, we integrate over the pre-crisis marginal distribu-
tion of sovereign bonds, yt,S ∼ N (µPC ,ΣPC), estimated with the pre-crisis sub-sample.
17Counterfactual decompositions have been standard in the labour literature to analyse the roleof institutional and labour market factors in accounting for changes in wage distributions. Prominentexamples include Dinardo et al. (1996), Gosling et al. (2000), and Machado and Mata (2005). The lattertwo papers use quantile regressions. More recently, Chernozhukov et al. (2013) provide estimation andinference procedures for a class of regression-based methods used to analyse counterfactual distributions;in particular, they provide results for quantile regressions.
19
In both cases we use the crisis conditional distribution gBi|S(·), whose parameters are
shown in Table 7.
Figure 9 presents the plots of the actual and counterfactual densities in December
2009 for three banks: BNP Paribas, Deutsche Bank, and Banco Santander. The higher
peaks at the center of the three counterfactual distributions indicate that the actual
densities are much more volatile and probably have fatter tails. In addition, the actual
densities for BNP Paribas and Banco Santander seem to have fatter left tails than those
of the counterfactual estimations. Table 9 presents the moments of the marginal densi-
ties, plus two often-used risk measures, the Value-at-Risk (VaR) and Expected Shortfall
(ES). We find that, for BNP and Banco Santander, the counterfactual densities have
positive mean returns, while the actual densities have negative mean returns. The stan-
dard deviations confirm that the counterfactual distributions are less volatile than the
actual distributions. Meanwhile, Deutsche Bank seems to have suffered a reduction in
its expected return, but the volatility of its distribution has been less affected by the
sovereign crisis. The tail risk measures that correspond to the actual densities of BNP
and Santander are also much higher than the counterfactual densities; these risk mea-
sures appear to be more insensitive to the sovereign crisis in the case of Deutsche Bank,
however. In sum, the results suggest that GIIPS and non-GIIPS banks were strongly
exposed to the financial crisis, while German banks, though they were hit, were more
insulated from the crisis.
6 Conclusions
With the European financial and sovereign debt crisis as the context, we investigate
the distributional linkages between sovereign bond returns and bank asset returns. Re-
sults from quantile regression estimates suggest that sovereign bond returns exhibit a
nonlinear contemporaneous dependence on the whole distribution of bank asset returns;
this feature is not captured by standard regressions, which focus on the conditional mean
of the distribution of bank asset returns. Specifically, we find positive, nonlinear depen-
dence from GIIPS sovereign bonds to banks headquartered in GIIPS countries. We also
observe evidence of positive, nonlinear dependence from peripheral sovereign bonds to
the entire distribution of non-peripheral sovereign bond returns. These results suggest
that there is contagion from peripheral to non-peripheral sovereign bonds. There is also
20
evidence of smaller dependence of bank returns on sovereign bond returns, although we
still find a significant impact of home bank returns on their country’s sovereign bond
returns for non-peripheral countries.
We then analyse the response of the conditional densities of banks to shocks in some
sovereign bond returns. To do so, we propose a weighted kernel density interpolation
methodology to recover conditional densities of bank asset returns given sovereign bond
returns. The results show that a negative shock to the peripheral sovereign bond returns
during crisis periods shifted the distribution of bank asset returns to the left (implying
a lower expected return), and increased negative skewness by reducing the right tail of
the distribution. The impact seems to be stronger on GIIPS banks.
In addition, we analyse how the conditional distributions evolve over time by ex-
tending the quantile model into a quantile vector autoregressive framework. The results
show that not only does the contemporaneous dependence from bond to bank returns
still hold, but also that this dependence is strongly persistent at the tails of the distri-
bution of bank asset returns. However, the contemporaneous link from bonds to banks
seems to be stronger on GIIPS banks, while non-GIIPS banks are more affected by lagged
dependence. We then study the evolution of the conditional distributions of bank asset
returns over time in response to a perturbation in some sovereign bond returns. The re-
sults indicate that the contemporaneous dependence has a more dominant impact in the
short run, which generates a level shift in banks’ asset returns conditional distributions.
In the long run, however, the main effect is an increase in the probability mass at the
tails.
We finally analyse the sensitivity of our results to the crisis by allowing the most
relevant parameters to change during the crisis. The results indicate that the dependence
between the peripheral sovereign bonds and non-peripheral bank asset returns is stronger
in crisis periods than in non-crisis periods. The same observation also holds true for
spillovers from own country bond to bank returns for GIIPS countries. We analyse a
scenario where we obtain the marginal density of a bank in the case that the sovereign
crisis had not occurred. The results indicate that, had the sovereign crisis not occurred,
bank returns would have had a higher expected return and a distribution with lower
volatility and thinner tails. Once again, the impact is particularly strong for GIIPS
banks, and weaker in relative terms for German banks.
21
The results provide evidence of the importance of higher-order moments when as-
sessing dependence between financial variables. Though it is apparent from the crisis
that there exists a feedback mechanism between sovereign bond and bank returns, which
has been referred to as the “diabolic loop” between sovereign bonds and banks (see
Acharya et al., 2014, Bolton and Jeanne, 2011, and Gennaioli et al., 2014 for theoretical
papers), our results do not have a causal interpretation. In particular, we do not study
what causes the sovereign-bank link, which may well be due to determinants from the
real economy (see Castro and Mencıa, 2014). Nevertheless, our results provide useful
information for market analysts and financial regulators, who are becoming increasingly
concerned about the systemic risk implications of multivariate dependence in the mar-
ket. Finally, our findings contain relevant insights for the literature on the relationship
between banking and sovereign crises, (see e.g. Reinhart and Rogoff, 2011). In particu-
lar, we show that the dependence between banks’ returns and sovereign debt behaves in
a highly nonlinear fashion. For instance, a bank’s return and a sovereign bond may be
negatively correlated in normal times, but their dependence may become positive during
a crisis. Hence, we quantify how the bank-sovereign link intensifies as the sovereign bond
moves to the tail of its return distribution.
Our results open some interesting questions for future research. It would be inter-
esting to explore the impact of the real economy on the non-linear dependence between
sovereign debt and banks’ returns. It might also be useful to extend our analysis to con-
sider quantile-based measures of higher-order moments and study which market factors
affect the evolution of asset return distributions over time, given that the literature has
established the importance of higher-order moments in asset pricing (see e.g. Harvey and
Siddique, 2000). Moreover, it could be helpful to extend the quantile regression frame-
work to analyse, in a more flexible manner, the impact of uncertainty in asset pricing
dynamics, as in Bansal and Yaron (2004). Lastly, it also might be interesting to consider
how government policy interventions have an impact on these conditional distributions.
22
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24
A List of Banks
This is a list of banks that are included in the dataset. The banks are classified
according to the country of its headquarters. We also include the identifier in Datastream
for each of the banks in the sample.
Bank Identifier Country
Erste Group Bank A.G. ERS Austria
KBC Group N.V. KB Belgium
Danske Bank DAB Denmark
BNP Paribas BNP France
Societe Generale SGE France
Deustche Bank A.G. DBK Germany
Commerzbank A.G. CBK Germany
National Bank of Greece ETE Greece
Alpha Bank PIST Greece
Piraeus Bank Group PEIR Greece
Allied Irish Banks plc ALBK Ireland
Bank of Ireland BKIR Ireland
Intesa Sanpaolo S.p.A ISP Italy
Unicredit S.p.A UCG Italy
ING Bank N.V. ING Netherlands
Banco Comercial Portugues, S.A. BCG Portugal
Banco Santander S.A. SCH Spain
Banco Bilbao Vizcaya Argentaria S.A. BBVA Spain
Nordea Bank A.B. NDA Sweden
Skandinaviska Enskilda Banken A.B. SEA Sweden
Svenska Handelsbanken A.B. SVK Sweden
Swedbank A.B. SWED Sweden
Credit Suisse Group A.G. CS Switzerland
UBS A.G. UBS Switzerland
Royal Bank of Scotland Group plc RBS United Kingdom
HSBC Holdings plc HSBC United Kingdom
Barclays plc BARC United Kingdom
25
B Model specification and estimation
B.1 Baseline model
We can write the matrices in (3) and (4) as Abb = νIn, Abs = αA11+βA21+γA31+
τA41, Asb = κA12 + πA22 + ηA32 + ωA42, and Ass = φIm + ψA52. These expressions
are based on auxiliar matrices, which are defined as follows:
1. GIIPS sovereign bond effect on non-GIIPS banks’ returns: A11 is an n×m matrix
such that A11(i, j) = 1 if country (bank i) /∈ GIIPS but country j ∈ GIIPS, and
zero otherwise.
2. German sovereign bond effect on non-German banks’ returns: A21 is an n × m
matrix such that A21(i, j) = 1 if country (bank i) /∈ DE but country j = DE, and
zero otherwise.
3. Own country effect on banks’ returns for non-GIIPS countries: A31 is an n ×m
matrix such that A31(i, j) = 1 if country (bank i) = country j, and country j /∈GIIPS, and zero otherwise.
4. Own country effect on banks’ returns for GIIPS countries: A41 is an n×m matrix
such that A41(i, j) = 1 if country (bank i) = country j, and country j ∈ GIIPS,
and zero otherwise.
5. Own bank effect on sovereign bond returns for non-GIIPS countries: A12 is an
m×n matrix such that A12(i, j) = 1 if country i = country (bank j), and country
j /∈ GIIPS, and zero otherwise.
6. Own bank effect on sovereign bond returns for GIIPS countries: A22 is an m× n
matrix such that A22(i, j) = 1 if country i = country (bank j), and country j ∈GIIPS, and zero otherwise.
7. GIIPS banks effect on non-GIIPS sovereign bond returns: A32 is an m×n matrix
such that A32(i, j) = 1 if country i /∈ GIIPS, but country (bank j) ∈ GIIPS, and
zero otherwise.
8. German bank effect on non-German sovereign bond returns: A42 is an m × n
matrix such that A42(i, j) = 1 if country i /∈ GIIPS, but country (bank j) = DE,
and zero otherwise.
26
9. GIIPS sovereign effect on non-GIIPS sovereign bond returns: A52 is an m × m
matrix such that A52(i, j) = 1 if country i /∈ GIIPS, but country j ∈ GIIPS, and
zero otherwise.
Hence, we can rewrite (3) and (4), respectively, as:
Note: The table provides regression results for the bond equation
qt,S(θ) = cS(θ) +Asb(θ)yt,B +Ass,PC(θ)yt,S · 1(t < T )
+Ass,C(θ)yt,S · 1(t ≥ T ) + φ(θ)yt−1,S ,
which denotes a quantile regression with pre-crisis (PC) and crisis (C) parameters for the GIIPS bond
to non-GIIPS bond effect. The dependent variables in these regressions are bank asset returns. The
first column corresponds to the effect of interest, while the second to the last columns correspond to
a particular quantile. The starting period for crisis times was designated as the first week of August
2007 (T in the equation). All regressions were under the time period from January 3, 2001-November
6, 2013, except for Greece, Ireland and Portugal. Standard errors are in parentheses, and are computed
by using a sandwich formula as outlined in White et al. (2013). Significance levels are indicated by the
following: ∗∗∗ - 1%,∗∗ - 5%, ∗ - 10%.
37
Table 9. Moments of the Marginal Densities and Risk Measures
BNP Paribas Deutsche Bank SantanderActual Counterfactual Actual Counterfactual Actual Counterfactual
Mean -0.0129 0.0266 0.0057 0.0464 -0.0111 0.0360Std. Dev. 3.5367 2.9030 2.5844 2.3967 3.3728 2.659195% - VaR 5.8345 4.8439 4.3462 4.1056 5.5765 4.470195% - ES 7.4341 5.8994 5.3521 4.7994 6.9487 5.3291
Note: This table shows the moments and some often-used risk measures of the actual and counterfactual
densities of the following banks: BNP Paribas, Deutsche Bank, and Banco Santander. The date chosen
for the analysis is December 2009.
38
Figure 1: Sovereign Bond Returns of Germany and GIIPS countries, 2007-2013
Jan07 Jan08 Jan09 Jan10 Jan11 Jan12 Jan13 Jan140
5
10
15
20
25
30
35
40
45
50
GermanyGreeceIrelandItalyPortugalSpain
1 2
3
4
Note: Sample period: January 3, 2007 - November 6, 2013. This illustrates the divergence between German and GIIPS 10-year sovereign bond yields during the
sovereign debt crisis, which began in late 2009. The dashed lines indicate significant periods in the financial and sovereign debt crises, marked with numbers: (1)
the Lehman brothers collapse, (2) the announcement of a 300-billion euro sovereign debt by Greece, (3) the rise in borrowing costs for Spain and Italy, and (4)
the announcement of Mario Draghi, ECB president, of the commitment to “preserve the euro”.
39
Figure 2: Return Volatility and Sovereign Bond Yields, 2007-2013
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